This one is a little bit like cheating, because I have discussed it with other trainers before, but we never succeeded in implementing it fully. It is also a little bit like Vesa's idea.
In this game, there is an approaching tropical cyclone, and you have to make decisions about evacuation of specific parts of the coastal regions, based on storm surge information and wind forecasts. The challenge is similar to other simulations, weighing the costs of evacuation and closing of facilities with the risks to human life and damage to property, considering on the uncertainties of the forecast of the cyclone evolution and path.
You could do similar games on longer time scales based on seasonal climate predictions and the decisions that need to be made by various industries, like agriculture and energy.
On shorter time scales, what about the prediction of convective storm morphology based on the atmospheric conditions. You have one minute to forecast location and severity of the storm in the next hour, for example. Who do you warn, and how severe is your warning?
Come to think of it, these are not so much games as just case study activities. When do they become games?
Patrick